Separability structures corresponding to conservative dynamical systems
type: Item
instance of: scholarly article
title: Separability structures corresponding to conservative dynamical systems
zbMATH Open document ID: 0573.70012
DOI: 10.1007/BF01556323
author: S. Benenti
author: Giorgio Pidello
published in: Meccanica
publication date: 1984-01-01T00:00:00Z
review text: Let (M,g) be a Riemannian manifold with the metric g of any signature. The authors consider the Hamiltonian H on \(T^*M\) of the type \(H=g^{ij}p_ ip_ j+V\quad\) \((g^{ij}\) are contravariant components of g, V is a function on M) and study the corresponding Hamilton-Jacobi equation. For H satisfying Levi-Cività separability conditions, suitable coordinates in charts (called normal separable coordinates) are constructed, in which \(g^{ij}\) and V assume an ''irreducible'' form. This leads to complete integrability of the Hamilton-Jacobi equation, which is obtained by the integration of the correspondent separated system of ordinary differential equations in normal separable coordinates.
Mathematics Subject Classification ID: 70H20
Mathematics Subject Classification ID: 70G45
Mathematics Subject Classification ID: 53B50
zbMATH DE Number: 3915684
zbMATH Keywords: Riemannian manifold
zbMATH Keywords: metric g of any signature
zbMATH Keywords: Levi-Cività separability conditions
zbMATH Keywords: normal separable coordinates
zbMATH Keywords: complete integrability
MaRDI profile type: Publication
cites work: Q4119759
cites work: Q3868412
cites work: Q3902137
cites work: Separation of variables in the Hamilton–Jacobi, Schrödinger, and related equations. I. Complete separation
cites work: Separation of variables in the Hamilton-Jacobi equation for non-conservative systems
description: scientific article; zbMATH DE number 3915684